The new Everton boss wants to beef up the Blues' attack following their summer sale of last season's top-scorer Romelu Lukaku and is considering a move to be reunited with the Belgium international, who played under him at Selhurst Park last season.

Big Sam is also heavily in the running for Sevilla’s Steven N'Zonzi and hopes to beat Arsenal to the £23million-rated midfielder.

Palace record-buy Benteke only scored his first goal of the season on Saturday (Image: AFP)

However, Big Sam will have to sell before he starts splashing out after Everton’s outlay under Ronald Koeman last summer.

The club shelled out a hefty £142.38m in the last window, though the sale of Lukaku to Manchester United for £76m and other outgoings reduced the net outlay to £45.75m.

Will Benteke return to Merseyside 18 months on from his one season with Liverpool? (Image: Liverpool FC via Getty)

However, Allardyce has been told he can’t bring in new players without offloading first.

Everton have a large contingent of midfielders already, but Allardyce and director of football Steve Walsh believe N’Zonzi would add an extra physical presence to the squad, as well as useful European experience.

The Frenchman, 29, is also on Arsene Wenger’s radar, but Allardyce hasn’t given up hope of again landing a player he bought in 2008 when he was manager at Blackburn and who cost Sevilla £7m when he joined from Stoke two years ago.

Big Sam even looked into whether uncapped N'Zonzi qualified for England on residency grounds after six years playing in the Premier League, during his brief spell last year as Three Lions manager.